Test with the following command for the webvtt subtitle:
$ ./ffmpeg -y -i input_with_subtitle.mkv \
 -b:v:0 5250k -c:v h264 -pix_fmt yuv420p -profile:v main -level 4.1 \
 -b:a:0 256k \
 -c:s webvtt -c:a mp2 -ar 48000 -ac 2 -map 0:v -map 0:a:0 -map 0:s:0 \
 -f hls -var_stream_map "v:0,a:0,s:0,sgroup:subtitle" \
 -master_pl_name master.m3u8 -t 300 -hls_time 10 -hls_init_time 4 -hls_list_size \
 10 -master_pl_publish_rate 10  -hls_flags \
 delete_segments+discont_start+split_by_time ./tmp/video.m3u8

Check the master m3u8:
$ cat tmp/master.m3u8
#EXTM3U
#EXT-X-VERSION:3
#EXT-X-MEDIA:TYPE=SUBTITLES,GROUP-ID="subtitle",NAME="subtitle_0",DEFAULT=YES,URI="video_vtt.m3u8"
#EXT-X-STREAM-INF:BANDWIDTH=6056600,RESOLUTION=1280x720,CODECS="avc1.4d4829,mp4a.40.33",SUBTITLES="subtitle"
video.m3u8

Check the result by convert to mkv:
$ ./ffmpeg -strict experimental -i ./tmp/master.m3u8 -c:v copy -c:a mp2 -c:s srt ./test.mkv
Signed-off-by: Limin Wang <lance.lmwang@gmail.com>